In string theory there are various limits where a non-perturbative description of quantum gravity can be obtained. These limits have been used to give precise countings of black hole microstates, which have matched expectations from black hole thermodynamics to ever-increasing precision (see [1]} for a particularly impressive recent match). The best-understood of these limits is the AdS/CFT correspondence, which says that quantum gravity in asymptotically-AdS space is equivalent to conformal field theory living at its asymptotic boundary. Initial studies of this correspondence were focused on using classical gravity in the “bulk” AdS description to study strongly-coupled dynamics in the boundary theory (see the following section), but in the last 15 years much progress has been made on understanding in more detail how the bulk spacetime emerges from the boundary description. A key early breakthrough was the Ryu-Takayanagi proposal, eventually refined into the quantum extremal surface (QES) formula, for computing the von Neumann entropy of a boundary state in terms of bulk quantities. This led to a broader understanding that boundary entanglement is a key element of the emergence of the bulk, which was eventually expressed mathematically in the idea that the correspondence should be understood as a quantum error-correcting code [2]}. In the last few years this program led to the remarkable discovery that the “Page curve” of an evaporating black hole can be reliably computed using the QES formula, with the result being just what is expected from a unitary evaporation process [3]}.
